advection/polynomial.h

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/**********************************************************************
 *  Copyright (C) 2011 - 2014 by the authors
 *  Distributed under the MIT License
 *
 * See the files AUTHORS and LICENSE in the project root directory
 **********************************************************************/
#ifndef __advection_polynomial_h
#define __advection_polynomial_h

#include <advection/parameters.h>
#include <amandus/integrator.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/tensor.h>
#include <deal.II/integrators/advection.h>
#include <deal.II/integrators/l2.h>

using namespace dealii;
using namespace LocalIntegrators;
using namespace MeshWorker;

namespace Advection
{
template <int dim>
class PolynomialRHS : public AmandusIntegrator<dim>
{
public:
  PolynomialRHS(const Parameters& par,
                const std::vector<Polynomials::Polynomial<double>> potentials_1d);

  virtual void cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void boundary(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;

private:
  dealii::SmartPointer<const Parameters, class PolynomialRHS<dim>> parameters;
  std::vector<Polynomials::Polynomial<double>> potentials_1d;

  std::vector<std::vector<double>> velocity;
};

template <int dim>
class PolynomialError : public AmandusIntegrator<dim>
{
public:
  PolynomialError(const Parameters& par,
                  const std::vector<Polynomials::Polynomial<double>> potentials_1d);

  virtual void cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void boundary(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const;
  virtual void face(DoFInfo<dim>& dinfo1, DoFInfo<dim>& dinfo2, IntegrationInfo<dim>& info1,
                    IntegrationInfo<dim>& info2) const;

private:
  dealii::SmartPointer<const Parameters, class PolynomialError<dim>> parameters;
  std::vector<Polynomials::Polynomial<double>> potentials_1d;
};

//----------------------------------------------------------------------//

template <int dim>
PolynomialRHS<dim>::PolynomialRHS(const Parameters& par,
                                  const std::vector<Polynomials::Polynomial<double>> potentials_1d)
  : parameters(&par)
  , potentials_1d(potentials_1d)
  , velocity(dim, std::vector<double>(1))
{
  this->use_boundary = true;
  this->use_face = false;
  velocity[0][0] = 1.;
  velocity[1][0] = 2.;
}

template <int dim>
void
PolynomialRHS<dim>::cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const
{
  std::vector<double> rhs(info.fe_values(0).n_quadrature_points, 0.);

  std::vector<double> px(2);
  std::vector<double> py(2);
  for (unsigned int k = 0; k < info.fe_values(0).n_quadrature_points; ++k)
  {
    const double x = info.fe_values(0).quadrature_point(k)(0);
    const double y = info.fe_values(0).quadrature_point(k)(1);
    potentials_1d[0].value(x, px);
    potentials_1d[0].value(y, py);

    rhs[k] = velocity[0][0] * px[1] * py[0] + velocity[1][0] * px[0] * py[1];
  }

  L2::L2(dinfo.vector(0).block(0), info.fe_values(0), rhs);
}

template <int dim>
void
PolynomialRHS<dim>::boundary(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const
{
  std::vector<double> rhs(info.fe_values(0).n_quadrature_points, 0.);
  std::vector<double> null(info.fe_values(0).n_quadrature_points, 0.);

  std::vector<double> px(2);
  std::vector<double> py(2);
  for (unsigned int k = 0; k < info.fe_values(0).n_quadrature_points; ++k)
  {
    const double x = info.fe_values(0).quadrature_point(k)(0);
    const double y = info.fe_values(0).quadrature_point(k)(1);
    potentials_1d[0].value(x, px);
    potentials_1d[0].value(y, py);

    rhs[k] = px[0] * py[0];
  }

  dealii::LocalIntegrators::Advection::upwind_value_residual(
    dinfo.vector(0).block(0), info.fe_values(0), null, rhs, velocity);
}

//----------------------------------------------------------------------//

template <int dim>
PolynomialError<dim>::PolynomialError(
  const Parameters& par, const std::vector<Polynomials::Polynomial<double>> potentials_1d)
  : parameters(&par)
  , potentials_1d(potentials_1d)
{
  this->use_boundary = false;
  this->use_face = false;
  this->error_types.push_back(2);
  this->error_types.push_back(2);
}

template <int dim>
void
PolynomialError<dim>::cell(DoFInfo<dim>& dinfo, IntegrationInfo<dim>& info) const
{
  Assert(dinfo.n_values() >= 2, ExcDimensionMismatch(dinfo.n_values(), 4));

  std::vector<double> px(3);
  std::vector<double> py(3);
  for (unsigned int k = 0; k < info.fe_values(0).n_quadrature_points; ++k)
  {
    const double x = info.fe_values(0).quadrature_point(k)(0);
    const double y = info.fe_values(0).quadrature_point(k)(1);
    potentials_1d[0].value(x, px);
    potentials_1d[0].value(y, py);
    const double dx = info.fe_values(0).JxW(k);

    Tensor<1, dim> Du = info.gradients[0][0][k];
    Du[0] -= px[1] * py[0];
    Du[1] -= px[0] * py[1];
    double u = info.values[0][0][k];
    u -= px[0] * py[0];

    // 0. L^2(u)
    dinfo.value(0) += (u * u) * dx;
    // 1. H^1(u)
    dinfo.value(1) += (Du * Du) * dx;
  }

  for (unsigned int i = 0; i < 2; ++i)
    dinfo.value(i) = std::sqrt(dinfo.value(i));
}

template <int dim>
void
PolynomialError<dim>::boundary(DoFInfo<dim>&, IntegrationInfo<dim>&) const
{
}

template <int dim>
void
PolynomialError<dim>::face(DoFInfo<dim>&, DoFInfo<dim>&, IntegrationInfo<dim>&,
                           IntegrationInfo<dim>&) const
{
}
}

#endif